Notes from Amartya Sen on Indian Calendars

The official Calendar Reform Committee, appointed in 1952 (shortly after Indian independence), which was chaired by Meghnad Saha himself, identified more than thirty well-developed calendars in systematic use in the country

The authoritative Whitaker’s Almanac reduces this long list to seven principal “Indian eras.” It also gives the translation of the Gregorian year 2000 into these selected major calendars.

The Gregorian year 2000 AD corresponds, Whitaker’s Almanac reports, respectively with: Year 6001 in the Kaliyuga calendar; Year 2544 in the Buddha Nirvana calendar; Year 2057 in the Vikram Samvat calendar; Year 1922 in the Saka calendar; Year 1921 (shown in terms of 5-yearly cycles) of the Vedanga Jyotisa calendar; Year 1407 in the Bengali San calendar; Year 1176 in the Kollam calendar.

First, the zero point of Kaliyuga is not 6001 but 5101 years ago (corresponding to 3101-3102 BC). Second, this zero point (5101 years ago) is most unlikely to have been the actual date of origin of this calendar.

Aryabhatta noted that 3600 years of the Kaliyuga calendar were just completed when he turned 23 (the year in which this precocious genius wrote his definitive mathematical treatise, known as Aryabhatiya).3 That was the year 421 in the Saka calendar, which overlapped with 499 AD. From this it can be readily worked out that 2000 AD corresponds to year 5101 in the Kaliyuga calendar

There is a clear discrepancy between the alleged astronomical observations (as reported for the zero year) and what would have been seen in the sky in 3102 BC.

Returning to the Kaliyuga calendar, it is also perhaps of some significance that there is no corroboration of the use of the Kaliyuga calendar in the Vedas, which are generally taken to date from the second millennium BC.

There is, in fact, plenty of calendrical discussions in the Vedas, and a clear exposition of a system in which each year consists of twelve months of 30 days, with a thirteenth (leap) month added every five years. While oldest of the Vedas, the Rigveda, outlines the main divisions of the solar year into months and seasons (four seasons of 90 days each), the more precise calculations, including the “leap” (or intercalary) months can be found in the Atharvaveda.

It appears that there is no overt or even covert reference to the Kaliyuga calendar in the Ramayana or the Mahabharata either. Consideration of this and other evidence even prompted Meghnad Saha and his collaborators in the Calendar Reform Committee to suggest that the Kaliyuga calendar might have taken its present form precisely at the time of Aryabhata, in 499 AD

The Vikram Samvat calendar, which is quite widely used in North India and in Gujarat, is traced to the reign of King Vikramaditya, and has a zero point at 57 BC.

The Saka calendar, which has a zero point (not necessarily its historical origin) in 78 AD, was in good use by 499 AD. Indeed, we know from Aryabhata’s own dating of the Kaliyuga in terms of the Saka era (421 Saka year) that at least by then the Saka era is well-known and in good use.

It is worth noting that the Badami inscription dating from 465 Saka era or 543 AD does confirm the use of the Saka era (not very long after the Aryabhata statement, dated at the 421st Saka year, or 499 AD).

The mathematician Varahamihira gave 365.25875 days as the true measure of the year, which while close enough, was still slightly wrong, since the length of the sidereal year is 365.25636 days and the tropical year is 365.24220 days. The errors have moved the different north Indian calendars away from the intended fixed points, such as the vernal equinox, but they have tended to move together, with considerable solidarity with each other.

The Vikram Samvat calendar (with a zero point in 57 BC) apparently originated in this ancient capital city of Ujjain. But it is also the locational base of the Saka system (zero point in 78 AD) and a great many other Indian calendars. Indeed, even today, Ujjain’s location is used to fix the anchor point of the Indian clock (serving, in this respect, as the Indian Greenwich). The Indian Standard Time that governs our lives still remains a close approximation of Ujjayini time — five hours and 30 minutes ahead of GMT.

A contemporary visitor to this very modest and sleepy town may find it interesting to note that nearly two millennia ago, the well-known astronomical work Paulisa Siddhanta, which preceded the definitive Aryabhatiya, focused its attention on longitudes at three places in the world: Ujjain, Benares and Alexandria. We have wonderful descriptions of Ujjayini in Indian literature, particularly from Kalidasa.